Existence of general mean square solutions for a sequential random fractional differential system with nonlocal conditions

Abstract

In this study, we discuss the existence of solutions for a coupled system of two- sequential random fractional differential equations involving nonlocal periodic boundary conditions. Using a version of Leray-Schauder alternative theorem, we present recent results on the existence of coupled solutions for the problem. The obtained solutions as well as their Caputo derivatives satisfy some stochastic processes properties. An illustrative example is also discussed at the end of this paper.

Subject Classification: (2010):

• 30C45
• 39B72
• 39B82

Keywords:

• Caputo derivative
• Sequential random differential equation
• Existence and uniqueness
• Coupled system
• Mean square solution